Let $\mathbf{X}$ $(p \times p)$ be a symmetric matrix. The vecp operator stacks the elements of $\mathbf{X}$ above and including the diagonal columnwise. The vech operator stacks the elements of $\mathbf{X}$ below and including the diagonal columnwise.
$$ \text{vecp}(\mathbf{X}) = \begin{pmatrix} x_{11} \\ x_{12} \\ x_{22} \\ \vdots \\ x_{1p} \\ \vdots \\x_{pp} \end{pmatrix} \quad \text{and} \quad \text{vech}(\mathbf{X}) = \begin{pmatrix} x_{11} \\ x_{21} \\ \vdots \\ x_{p1} \\ x_{22} \\ \vdots \\ x_{p2} \\ \vdots \\x_{pp} \end{pmatrix}. $$
Now let $\mathbf{A}$ and $\mathbf{B}$ be the unique matrices defined by $\text{vec}(\mathbf{X})= \mathbf{A} \text{vecp}(\mathbf{X})$ and $\text{vec}(\mathbf{X})= \mathbf{B} \text{vech}(\mathbf{X})$, respectively.
How are the matrices $\mathbf{A}$ and $\mathbf{B}$ related?